Nice writeup bro!
My experience on this:
Using normal paint polishes, as per your result, doesn't fully remove.
Use Acid based cleaners (StainX), fast and effective, but risky. If the glass has been treated by using those powder type watermark remover + 3M sanding sponge (Rainaway style), and you use Stain X after that to remove new watermarks, it will haze the glass slightly because the 3M sanding sponge leaves very very fine scratches and the acid somehow will haze the glass. So the danger is not knowing whether or not the glass has been 'scoured' before. I have been using this combo also but it will leave some scratches in the glass when inspected with high lumens LED light.
Now my fav combo is Sonax/Osren Felt Pad and an abrasive glass polish (Sonax Profiline Glass Polish / CarPro Ceriglass / Osren Glass Polish Cream) polished with DA polisher. Removes all watermarks, without putting any new scratches in. You should try this if you have the chance. Downside is it takes more time compared to acid.